# Re: Discussion Question 2 - [Channel-talkmathhs] Teaching Mathgrades 9-12

From: Janet von Stein <tristar5@optonline.net>
Date: Sun Apr 17 2005 - 18:51:22 EDT
X-Mailer: Microsoft Outlook Express 6.00.2900.2180

Hi Liz:

I completed session 3 and have been thinking about problem lessons.
I don't think we talked about what grades we teach but I teach 9th grade in
NY. Currently this is called Math A. It is an integrated course of
primarily algebra, with geometry, discrete, and logic.
A nice problem based lesson around this time of year is having students
identify what type of function most closely resembles the data collected and
graphed.

Activity 1 How Does Your Corn GROW?

Students plant corn. After seeds sprout the plants are measured each day
for a week and growth is recorded, entered into graphing calculators and
graphed as scatterplots. Students must decide on domain and range
(independent and dependent variable) so all points appear in window.

Students then analyze data and decide what type of function the data most
closely represent and write and equation to fit the data.

Students should be encouraged to make predictions about future growth of
plants.

Activity 2 ELIM&MINATION
Pour a 1/2 pound bag of M&Ms onto a paper plate in a single layer. Remove
M&Ms with the M showing on one side. Count and record the number of M&Ms
removed and pout the ones remaining into a container. Shake the container
and pour these M&Ms back onto the plat and again remove all M&Ms with the M
showing. Record the number removed and the number remaining . Continue to
repeat process until all M&M's are removed. Use the following chart to
record information. dd additional trial numbers as the experiment
progresses.
Trial Number Number Removed
Number Remaining
1.
2.
3.
etc.

Let x be the trial number and let y be the number of pieces remaining. Plot
all point (x,y) and analyze data. Make a scateerplot of each set of data on
calculator and decide which type of funciton best represents the data.
Write an equation that fits the data as closely possible. Test equations by
drawing the function over the scatterplot on the graphing caluculator.
Record the type of function you chose, the equation .

Activity 3
Flaming Function

Use smallest sized candles available and don't place the ruler too close to
the flame.

Let x be time in seconds and y be height in centimeters. Let the initial
value of x be zero and the initial value of y be the height of a birthday
candles. Stand the candles on a heat-resistant tile of plate by lighting
another candle and ripping some wax onto the plate and then setting the
candles in the wax. Light the candles and measure its height every twenty
seconds. Extinguish the candles before it burns all the way down. Plot the
ordered pairs (x,y) and analyze the data.

Activty 4 All Boxed In
Take a 20cm x 20cm piece of grid paper and cut congruent squares form each
corener. FOld up the sides to form a rectangular shaped box with no lid.
Determine the volume of the box and complete the folowing chart. Repeat
this process on another 20cm by 20cm piece of gridpaper for several
different sized cut square.

Height (cm) Length Width Volume
(cm^3)

Let x be the height of the box and let y be the volume ofthe box. Plot the
ordered airs (x,y) and anlayze the data.

Activity 5 Weather It's a Function

Most years have 365 days. Day 1 is Jan. 1, Jan 15 is day 15, Feb. 1 is day
32 etc. Determine whether a relationship exists between the number o the
day of the year and the normal high temperature for that day for the first
and fifteeenth days of each month. Use weather data from your locl area.
Let x be the number o the day of the year and y be the normal high
temperature on that day. Plot all ordered pairs (x,y) and analyze the data.
The following chart format can be used.
Day Temperature

Activity 6 Water Level
Fill a gallong jug with a spigot with water. Measure the depth of the water
in millimeters. Open the spigot for 15 seconds and measure the depth of the
water again. Repeat this process until the water is at the level of the
spigot. Let x be the total time the spigot was turned on in seconds (s) and
let y be the depth of the water in millimeters. Plot the ordered pairs
(x,y) and analyze the data using the following chart format.
Time (s) Depth (mm)

Activity 1 linear
Activity 2 Exponential Decay
Activity 3 Linear
Activity 5 Trigonometric

This comes from the Mathematics Teacher. Algebrai 1 students don't see
Trigonometric functions at this point but if you teach Algebra 2/Trig. or
Precalc it would be appropriate to include.

Jan

----- Original Message -----
From: "O'Hares" <ohares3@yahoo.com>
To: "Discussion list for TEACHING MATH, GRADES 9-12"
<channel-talkmathhs@learner.org>
Sent: Sunday, April 10, 2005 8:26 PM
Subject: Re: Discussion Question 2 - [Channel-talkmathhs] Teaching

> Janet,
>
> How are you? Would you like to work on a collaborative
> lesson plan effort for assignment 3-E? Or at least
> evaluate each others? Whatever you think...
>
> Liz
>
>
> --- O'Hares <ohares3@yahoo.com> wrote:
>
>> Janet,
>> It sounds like you offer your students a great
>> amount
>> of self-learning and self-disciplining techniques. I
>> always use a reflective journal. Sometimes I have
>> them
>> write some consider some prefacing questions on a
>> newly introduced lesson.
>>
>> Liz
>>
>>
>> --- Janet von Stein <tristar5@optonline.net> wrote:
>> > My students are paired at all times. (I have
>> tables
>> > for 2) Sometimes they
>> > work in groups of 3-4. I encourage them to ask
>> each
>> > other for help before
>> > they ask me (I like the ask 3 before me approach).
>> > Communication between
>> > students is very "telling". I like to go around
>> and
>> > listen as one student
>> > explains to another. If they can clearly explain
>> > something to another
>> > student they reinforce their own understanding.
>> I
>> > have my students keep
>> > math journals and frequently use exit reflections
>> at
>> > the end of a lesson.
>> > This is another opportunity to get an inside view
>> of
>> > their understanding. I
>> > can often get to the heart of misconceptions by
>> > listening to a student.
>> > Working in a group where they have to justify
>> their
>> > results prepares them
>> > for the work place when they may have to work as a
>> > group and convince their
>> > group members. I also think it is vital that
>> > students see connections to
>> > the real world for application of the mathematics.
>>
>> > Pointless algebraic
>> > manipulation serves no purpose. Some students are
>> > very adept at it but
>> > haven't a clue as to how a
>> > linear/quadratic/exponential or logrithmic
>> > equation relates to a real world situation. We
>> talk
>> > "ALOT" about what kind
>> > of model would fit the data.
>> > My overarching theme is How Can The Study of
>> > Mathematics Help To Make Sense
>> > of My World? & What Do Mathematicians Study?
>> > Patterns and Statistics are
>> > primary to their study in 9th Grade math.
>> >
>> > ----- Original Message -----
>> > From: "O'Hares" <ohares3@yahoo.com>
>> > To: "O'Hares" <ohares3@yahoo.com>; "Discussion
>> list
>> > for TEACHING MATH,
>> > GRADES 9-12" <channel-talkmathhs@learner.org>
>> > Sent: Monday, April 04, 2005 6:38 AM
>> > Subject: Discussion Question 2 -
>> > [Channel-talkmathhs] Teaching Math grades
>> > 9-12
>> >
>> >
>> > > DQ1: From Session 1 - Questions to write and
>> > reflect
>> > > about:
>> > >
>> > > What types of mathematical communication are you
>> > > interested in trying in your own classroom? How
>> > will
>> > > you go about doing that? What are you hoping to
>> > gain
>> > > from this work?
>> > >
>> > > Liz's Response: I would like to teach that there
>> > are
>> > > patterns everywhere and statistics that help us
>> > > understand these patterns. I think realistic
>> > student
>> > > activites involving banking and sales
>> experiments
>> > > using computers and technology can help me teach
>> > > these. This type of learning will encourage
>> > > multi-faceted communication, including student
>> to
>> > > cyberspace and back, and help break away from
>> the
>> > > instructor-led only model.
>> > >
>> > >
>> > >
>> > >
>> > >
>> > > __________________________________
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>> > >
>> > > _______________________________________________
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>> > >
>> >
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